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Research Areas & Groups

In the Department of Mathematics, our research ranges from laying theoretical foundations to working directly on real-world applications. Some of our faculty have collaborated with industry partners, governmental agencies and research institutes such as the Fields Institute for Research in Mathematical Sciences. We work under three main groups, within which current research areas include:

  • Biomathematics and biostatistics
  • Complex networks and graph theory
  • Computer security and cryptography
  • Data mining
  • Differential equations and operator theory
  • Financial mathematics
  • Fluid mechanics
  • Foundations of statistical mechanics
  • Machine Learning
  • Software Testing

Biomathematics and Fluids Group

Illustration of interconnected webs over the globe.

Our research team is currently focusing on applying mathematical techniques to the study of fluids, biology, medicine and health. We develop mathematical models and numeric computations within a range of specialties, including:

  • Blood flow
  • Oncology and immunology
  • Body mechanics
  • Interfacial instability in liquid films
  • Computational biology
  • Stochastic dynamics

Learn more about the team and our research. Visit our Biomathematics and Fluids Research Group website.

Computational Statistics

Led by Dr. You Liang, the Computational Statistics lab conducts significant methodological and applied research with real-world applications. Contemporary statistics is heavily data-driven. Data structures are often complicated — data alone may not easily translate into usable information. Our lab focuses on how to properly collect, process and analyze deep data to extract valuable insights and generate practical solutions.

Unlike other areas of mathematics, our emphasis is given to comprehensive and reproducible computational or statistical research, including data-driven methodology and algorithms. Our work relies heavily on computation and coding (in R, Matlab, Python), knowledge of data science, and skill in communicating with domain experts. 

Two current, major research projects include: 

  • Financial time series prediction: developing approaches to analyze the movement of financial data over successive time periods. Our findings have applications in portfolio optimization, algorithmic trading, options pricing, and demand and supply chain forecasting.
  • Hyperspectral image data analysis: extracting data not simply from numbers but from images, with particular focus on biomedical images and proteomics data. Our lab is currently collaborating on this long-term project with researchers at the University of Toronto and St. Michael’s Hospital, with funding from the Canadian Space Agency, the Fields Institute, and the ALS Society of Canada and the Brain Canada Foundation.

Image designed by Freepik

Financial Mathematics Research Group

Financial chart hologram with abstract background. Double exposure. Concept of market analysis

As one of the first schools to develop finance-specific degree programs, Toronto Metropolitan University also hosts one of Canada’s largest research groups in financial mathematics. We use mathematical tools to develop and calibrate mathematical models for financial transactions, and also explore emerging, cutting-edge areas in the field, including:

  • FinTech, machine learning and blockchain
  • Environmental finance and climate change risk
  • Derivative pricing
  • Portfolio optimization

Meet our team and explore our research. Visit our Financial Mathematics Research Group website.

Graphs at Ryerson

Graph representation of the similarity relationships derived from the database of Last.fm.

Graphs @ Ryerson (G@R) works in both pure and applied graph theory. Our research focuses on a variety of topics, such as modelling complex networks, searching networks, combinatorial designs, infinite graphs, and random graphs.

  • Industrial mathematics
  • Optimization
  • Graph searching and complex networks
  • Design theory
  • Model theory
  • Computational geometry
  • Probabilistic methods

For more information about the team, our research projects and upcoming seminars, visit our Graphs at Ryerson website.

Mathematics Education Lab (MathEdLab)

Dr. Francis Duah researches how undergraduate mathematics is taught and learned based on the assumption that learning and teaching university mathematics has unique challenges and differences from pedagogy in other disciplines. Dr. Duah’s research aims at findings and applications with direct impact on student retention and quality of course delivery.

The Mathematics Education Lab (MathEdLab) uses quantitative and qualitative educational and social research methods and data; interdisciplinary collaborations with psychologists, sociologists, and educators; community discussions; and pilot projects with technology industry partners to explore current topics, which include:

  • Transitions in undergraduate mathematics: Focusing on use of learning outcomes in course design and its impact on student achievement and resilience, particularly during students' move into advanced mathematics.
  • Mathematics pedagogy: Investigating open-education resources (OER) in the public domain — e.g. Youtube videos, open libraries, test banks, etc. — their use and impact on both self-motivated learning as well as behaviours such as academic integrity transgressions.
  • Widening participation in mathematical sciences: Exploring the reasons behind low diversity in advanced mathematics, despite its excellent potential to facilitate upward social mobility. Currently examining the relation between underrepresented populations and public perceptions of mathematics as a profession.

Visit Dr. Duah’s lab website, external link.

RAMLab

RAMLab is our state-of-the-art laboratory. It is equipped for developing mathematical models and numerical methods for applications in science and engineering. RAMLab encourages multidisciplinary exchanges with the scientific community at large, and is also an important component in training students and research assistants from various programs.